Relative separation axioms via semi-open sets
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 11-18.

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The concept of relative topological properties was introduced by Arhangel'skii and Gennedi and was subsequently investigated by many authors for different notions of general topology. In this paper few semi-separation axioms in relative sense are introduced and studied by utilizing semi-open sets. Characterizations and preservation under mapping of these newly defined notions are provided. Relationship that exists between these notions, with some of the absolute properties and with the existing relative separation axioms are investigated.
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Sehar Shakeel Raina; A. K. Das. Relative separation axioms via semi-open sets. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 11-18. https://geodesic-test.mathdoc.fr/item/BASM_2023_2_a1/

[1] Arhangel'skii A. V., Gennedi H.M.M., “Beginnings of the Theory of Relative Topological Properties”, General Topology, Spaces and Mappings, MGU, M., 1989, 3–48 | MR

[2] Arhangel'skii A. V., “Relative topological properties and relative topological spaces”, Topology Appl., 70 (1996), 87–99 | DOI | MR | Zbl

[3] Arhangel'skii A. V., “Relative normality and dense subspaces”, Topology and its Applications, 123 (2002), 27–36 | DOI | MR | Zbl

[4] Arhangel'skii A. V., Ludwig L., “On $\alpha$-normal and $\beta$-normal spaces”, Comment. Math. Univ. Carolin., 42 (2001), 507–519 | MR | Zbl

[5] Biswas N., “On Some Mappings in Topological Spaces”, Bull. Calcutta Math. Soc., 61 (1970), 127–135 | MR

[6] Crossley S. G., Hildebrand S. K., “Semi-closure”, Texas J. Sci., 2 (1971), 99–112

[7] Crossley S. G., Hildebrand S. K., “Semi-topological properties”, Fund. Math., 74 (1972), 233–254 | DOI | MR | Zbl

[8] Das A. K., Bhat P., Tartir J. K., “On a Simultaneous Generalization of $\beta$-Normality and Almost Normality”, Filomat., 31:1 (2017), 425–430 | DOI | MR | Zbl

[9] Das A. K., Raina S. S., “On Relative $\beta$-Normality”, Acta Math. Hungar., 160:2 (2020), 468–477 | DOI | MR | Zbl

[10] Dorsett C., “S-Normal and S-regular spaces”, Bull. Math. Soc. Sci. Math. R. S. Roumanie (NS), 26(74):3 (1982), 231–235 | MR | Zbl

[11] Hamlett T. R., “The property of being a Baire space is semi-topological”, Math. Chronicle, 5 (1977), 166–167 | MR | Zbl

[12] Just W., Tartir J. K., “A $\kappa$-normal not densely normal Tychonoff space”, Proc. Amer. Math. Soc., 127:3 (1999), 901–905 | DOI | MR | Zbl

[13] Kuratowski K., Topologie, v. I, Hafner, New York, 1958 | MR

[14] Levine N., “Semi-open sets and Semi-Continuity in topological spaces”, Amer. Math. Monthly, 70 (1963), 36–41 | DOI | MR | Zbl

[15] Maheshwari S. N., Prasad R., “Some new separation axioms”, Ann. Soc. Sci. Bruxelles. Ser. I, 89:3 (1975), 395–402 | MR | Zbl

[16] Maheshwari S. N., Prasad R., “On s-regular spaces”, Glasnik Mat. Ser. III, 10(30):2 (1975), 347–350 | MR | Zbl

[17] Maheshwari S. N., Prasad R., “On s-normal spaces”, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.), 22(70):1 (1978), 27–29 | MR | Zbl

[18] Nayar M. P., Arya S. P., “Semi-topological properties”, Internat. J. Math. Math. Sci., 15:2 (1992), 267–272 | DOI | MR | Zbl

[19] Noiri T., “A Generalization of Closed Mappings”, Atti. Accad. Naz. Lincei Rend. Ci. Sci Fis. Mat. Natur., 54 (1973), 412–415 | MR

[20] Raina S. S., Das A. K., “Some Variants of Normality in Relative Topological Spaces”, Filomat, 36:12 (2022), 4241–4249 | DOI | MR

[21] Steen L.A., Seebach J. A., Counter Examples in Topology, Springer Verlag, New York, 1978 | MR

[22] Willard S., General topology, Addison-Wesley pub. Co., Menlo Park, California, 1970 | MR | Zbl